"Dualities for the Domany-Kinzel model",
( with Makoto Katori, Norio Konno and Aiden Sudbury)
Journal of Theoretical Probability, 17(2004), 131-144.
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We study the Domany-Kinzel model, which is
a class of discrete-time Markov processes in one-dimension with two parameters
(p1, p2) [0,1]^2. When p1= and p2=(2-^2)
with (, ) [0,1]^2, the process
can be identified with the mixed site-bond oriented percolation model
on a square lattice with probabilities of a site being open and
of a bond being open.
This paper treats dualities for the Domany-Kinzel model ^A_t
and the DKdual ^A_t@starting from A. We prove that
(i) E(x^{|^A_t B|}) = E(x^{|^B_t A|}) if x=1 - (2p1-p2)/p1 ^2,
(ii) E(x^{|^A_t B|}) = E(x^{|^B_t A|}) if x=1 - (2p1-p2)/p1,
and
(iii) E(x^{|^A_t B|}) = E(x^{|^B_t A|}) if x=1 - (2p1-p2),
as long as one of A, B is finite and p2 <= p1.
